Question

Three point charges $+\,q,-2q$ and $+q$ are placed at points $(x=0,y=a,z=0),$ $(x=0,y=0,z=0)$ and $(x=a,y=0,z=0),$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are

• A. $\sqrt{2}\,qa$ along $+y$ direction
• B. $\sqrt{2}qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
• C. $qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
• D. $\sqrt{2}qa$ along $+x$ direction

Answer 1

Answer: (B)

$\sqrt{2}qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$

Answer 2

Key Idea Electric dipole moment is a vector quantity directed from negative charge to the similar positive charge. Choose the three coordinate axes as $x,\text{ }y$ and $z$ and plot the charges with the given coordinates as shown. O is the origin at which $-2\text{ }q$ charge is placed. The system is equivalent to two dipoles along $x$ and $y-$ directions respectively. The dipole moments of two dipoles are shown in figure.The resultant dipole moment will be directed along OP where $P=(a,a,0).$ The magnitude of resultant dipole moment is $p'=\sqrt{{{p}^{2}}+{{p}^{2}}}=\sqrt{{{(qa)}^{2}}+{{(qa)}^{2}}}$ $=\sqrt{2}\,qa$